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%I #12 May 23 2016 22:02:36
%S 0,1,10,12,2,3,4,5,6,7,8,9,21,20,22,23,24,25,26,13,31,27,41,28,29,14,
%T 30,32,15,33,34,51,35,36,37,61,38,39,40,42,16,43,44,45,46,17,47,48,49,
%U 50,52,53,54,55,56,57,18,58,59,60,62,63,64,65,66,67,71,68,69,70,72,73,74,75,76,77,78,79,19,80,82,83,84,85,86,87,88,89
%N The successive numbers of digits between two "1"s in the sequence are given by the sequence itself.
%C This is the lexicographically first such sequence, starting with a(1)=0 that has always been extended with the smallest integer not already present in the sequence and not leading to a contradiction.
%e There are 0 digits between the first two "1" of the sequence [0,1,10,]; then there is 1 digit between the next pair of "1" [10,12,]; then there are 10 digits between the next pair of "1" [12,2,3,4,5,6,7,8,9,21]; then there are 12 digits between the next pair of "1" [21,20,22,23,24,25,26,13]; then there are 2 digits between the next pair of "1" [13,31], etc. The quantities 0, 1, 10, 12, 2,... rebuild the starting sequence.
%K nonn,base
%O 1,3
%A _Eric Angelini_, May 23 2016